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Erschienen in:
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2021 | OriginalPaper | Buchkapitel

An Introduction to Maximal Regularity for Parabolic Evolution Equations

verfasst von : Robert Denk

Erschienen in: Nonlinear Partial Differential Equations for Future Applications

Verlag: Springer Singapore

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Abstract

In this note, we give an introduction to the concept of maximal \(L^p\)-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the connection to Fourier multipliers and \(\mathcal {R}\)-boundedness. The abstract results are applied to a large class of parabolic systems in the whole space and to general parabolic boundary value problems. For this, both the construction of solution operators for boundary value problems and a characterization of trace spaces of Sobolev spaces are discussed. For the nonlinear equation, we obtain local in time well-posedness in appropriately chosen Sobolev spaces. This manuscript is based on known results and consists of an extended version of lecture notes on this topic.

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Nächstes Kapitel On Stability and Bifurcation in Parallel Flows of Compressible Navier-Stokes Equations
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Metadaten
Titel
An Introduction to Maximal Regularity for Parabolic Evolution Equations
verfasst von
Robert Denk
Copyright-Jahr
2021
Verlag
Springer Singapore
Buch
Nonlinear Partial Differential Equations for Future Applications

Print ISBN: 978-981-334-821-9

Electronic ISBN: 978-981-334-822-6

Copyright-Jahr: 2021

DOI
https://doi.org/10.1007/978-981-33-4822-6_1